Inexact Chance-Constrained Linear Programming Model for Optimal Water Pollution Management at the Watershed Scale

An inexact chance-constrained linear programming (ICCLP) model for optimal water pollution management at the watershed scale was developed. We selected the net expenditures of the alternative strategies, including initial capital investment and operating costs, as the objectives of water pollution management. The total environmental capacity of the water bodies at different probability levels $\left(q_i\right)$ was considered a key constraint; other constraints included in the model were government minimum requirements on farmland area, land cover, treatment rate of domestic wastewater and rural wastes, and certain technical constraints. The ICCLP model was applied to Lake Qionghai watershed in China for water quality improvement with the goal of achieving a minimum total cost. Alternative strategies were incorporated following discussions with shareholders and experts. A three-period optimization was conducted based on the alternative strategies; the model parameters were based on field investigations. Five probability levels were considered in the model: $q_i=0.01$ , 0.25, 0.50. 0.90, and 0.99. The model results showed that the total optimized costs were between US $\$[55,710.86,80,691.81]\times {10}^4$ and US $\$[72,151.39,101,338.6]\times {10}^4$ under different probability levels. The model results indicate that soil erosion treatment, nonpoint source control measures, and rural waste treatment have much higher costs than other strategies, and our findings indicate that the ICCLP model can effectively deal with optimal water pollution management under uncertainty at the watershed scale.